Soldiers battling Abu Sayyaf in central Philippines are reported to have killed a key commander of the armed group who had been blamed for the beheadings of two Canadians and a German hostage.

Military chief of staff General Eduardo Ano said troops recovered and identified the remains of Moammar Askali, also known as Abu Rami, at the scene of the battle in a coastal village on Bohol island on Tuesday.

Five other Abu Sayyaf members were killed, along with four soldiers and policemen.

Ano said troops took the picture of Askali after his death and that captured Abu Sayyaf fighters identified the the young commander.

"This is a major blow to the Abu Sayyaf," Ano told AP news agency. "If they have further plans to kidnap innocent people somewhere, they will now have to think twice."

He said Askali had led several fighters, who travelled by speedboats from their jungle hideouts in the southern Sulu province to Bohol, in an apparent bid to carry out another kidnapping in a region that is popular for its beach resorts and wildlife.

Sporadic gun battles between the remaining Abu Sayyaf fighters and government forces continued on Wednesday, military officials said.

At least 10 people has been killed since Tuesday in the fighting in Bohol, far from the group's southern jungle bases.

Military officials say at least six fighters, three soldiers and a policeman have died in the ongoing gun battle in a village in the coastal town of Inabanga.

Abu Sayyaf fighters have crossed the sea border with Malaysia on powerful speedboats and kidnapped scores of foreign tourists in past years.

In 2001, they sailed as far as western Palawan province, where they seized 20 people from a resort.

Philippine President Rodrigo Duterte has ordered troops to destroy the group in Sulu and in outlying island provinces, and has threatened to declare martial law in the country's south if the threat posed by the Abu Sayyaf and other groups aligned with the Islamic State of Iraq and the Levant (ISIL) gets out of control.

Abu Sayyaf is still holding at least 29 captives in Sulu's jungles, many of them foreign tugboat and cargo ship crewmen seized at the sea border between the southern Philippines, Malaysia and Indonesia.